Ocean g-modes on rotating neutron stars

We recently argued that neutron stars accreting at rates greater than or similar to 10(-9) M. yr(-1) (the ''Z'' sources) are covered with massive oceans, and conjectured that waves in these oceans might modulate the outgoing X-ray flux at frequencies comparable to what is observed. For slowly rotating neutron stars, we showed that the low radial order (n similar to 1-2) g-mode oscillations are in the 5-8 Hz range for l = 1, in rough agreement with the ubiquitous similar to 6 Hz quasi-periodic oscillations (QPOs) seen in the Z sources. We now extend the thermal g-mode calculations to the case of rapidly rotating stars. The m = 0 modes are most relevant, since the m not equal 0 modes will necessarily acquire a high frequency in the observer's nonrotating frame. For spin frequencies Omega much greater than omega we find that the lowest m = 0 g-mode frequency is omega = 2(1/4)(Omega omega(1,0))(1/2), where omega(1,0) is the corresponding nonrotating l = 1 g-mode frequency. In the context of nonradial thermal g-modes, there are two ways to explain the fact that all six Z sources show similar to 6 Hz QPOs: (1) the neutron stars are all spinning at frequencies less than or similar to 6 Hz and a low-order (i.e., only a few radial nodes) g-mode is responsible for the oscillations, or (2) the g-mode is of higher radial order (n similar to 10-50) and is brought to similar to 6 Hz by fast rotation, thus requiring that all six neutron stars have rotation frequencies within a factor of 2-3 of each other. Which radial order, if any, the star chooses to excite is not known at present.